A researcher in a city with a large public train system wondered if the rent prices of one-bedroom apartments was related to the distance from the nearest train station. From a list of 250 similarly-sized one-bedroom apartments in the city, the researcher selected a simple random sample of 20 apartments. The researcher then measured the walking distance, in minutes, to the nearest train station and created a scatterplot comparing the walking distances to the advertised weekly rent, in dollars. A scatterplot and the output from computer regression software are shown below.
a. Explain a procedure by which the researcher may have selected the simple random sample.
b. Describe the association between walking distance from the nearest train station and weekly rent for the apartments included in the sample.
c. Interpret the value of the coefficient of determination (r-squared) in the context of this problem.
d. Before examining the data, a second researcher makes a prediction that for each additional minute of walking distance, the weekly rent will decrease by approximately $2. A 95% confidence interval for the slope of the regression line is constructed from the data, and is found to be (-2.471, -1.845). Does the confidence interval contradict the researcher’s claim? Justify your answer.
e. The second researcher wants to conduct a similar study to the first researcher. However, in the second researcher’s study, a mixture of one, two, and three-bedroom apartments were selected. Do you expect the value of r-squared for the second study to be greater than, less than, or equal to the value of r-squared in the first study? Justify your response.